Respuesta :
Given:
Two cards are drawn without replacement from a standard deck of 52 playing cards.
Required:
Find the probability of choosing a diamond for the second card drawn, if the first card, drawn with replacement, was a club.
Explanation:
The total number of cards in the deck = 52
The number of diamonds cards = 13
The number of club cards = 13
The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The probability that the first card is a club:
[tex]\begin{gathered} =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]If the drawn first card is not replaced then the left card is = 51
The probability that the second card is a diamond :
[tex]=\frac{13}{51}[/tex]Now the probability of choosing two cards, if the first is a club and the second is a diamond:
[tex]\begin{gathered} =\frac{1}{4}\times\frac{13}{51} \\ =\frac{13}{204} \\ =0.0637 \end{gathered}[/tex]Final answer:
The required answer is 0.0637.
